Interest Rate Risk I Chapter 8 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. K. R. Stanton

McGraw-Hill/Irwin 8-2 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Overview  This chapter discusses the interest rate risk associated with financial intermediation: Federal Reserve monetary policy Repricing model Maturity model Duration model *Term structure of interest rate risk *Theories of the term structure of interest rates

McGraw-Hill/Irwin 8-3 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Central Bank & Interest Rate Risk  Federal Reserve Bank: U.S. central bank Open market operations influence money supply, inflation, and interest rates  Targeting of bank reserves in U.S. proved disastrous  Oct-1979 to Oct-1982, nonborrowed reserves target regime.  Implications of reserves target policy: Increases importance of measuring and managing interest rate risk.

McGraw-Hill/Irwin 8-4 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Central Bank and Interest Rate Risk  Effects of interest rate targeting. Lessens interest rate risk  Greenspan view: Risk Management Focus on Federal Funds Rate Simple announcement of Fed Funds increase, decrease, or no change.

McGraw-Hill/Irwin 8-5 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Repricing Model  Repricing or funding gap model based on book value.  Contrasts with market value-based maturity and duration models recommended by the Bank for International Settlements (BIS).  Rate sensitivity means time to repricing.  Repricing gap is the difference between the rate sensitivity of each asset and the rate sensitivity of each liability: RSA - RSL.  Refinancing risk

McGraw-Hill/Irwin 8-6 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Maturity Buckets  Commercial banks must report repricing gaps for assets and liabilities with maturities of: One day. More than one day to three months. More than 3 three months to six months. More than six months to twelve months. More than one year to five years. Over five years.

McGraw-Hill/Irwin 8-7 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Repricing Gap Example AssetsLiabilities GapCum. Gap 1-day $ 20 $ 30 $-10 $-10 >1day-3mos >3mos.-6mos >6mos.-12mos >1yr.-5yrs >5 years

McGraw-Hill/Irwin 8-8 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Applying the Repricing Model   NII i = (GAP i )  R i = (RSA i - RSL i )  r i Example: In the one day bucket, gap is -$10 million. If rates rise by 1%,  NII (1) = (-$10 million) ×.01 = -$100,000.

McGraw-Hill/Irwin 8-9 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Applying the Repricing Model  Example II: If we consider the cumulative 1-year gap,   NII = (CGAP one year )  R = (-$15 million)(.01) = -$150,000.

McGraw-Hill/Irwin 8-10 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Rate-Sensitive Assets  Examples from hypothetical balance sheet: Short-term consumer loans. If repriced at year- end, would just make one-year cutoff. Three-month T-bills repriced on maturity every 3 months. Six-month T-notes repriced on maturity every 6 months. 30-year floating-rate mortgages repriced (rate reset) every 9 months.

McGraw-Hill/Irwin 8-11 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Rate-Sensitive Liabilities  RSLs bucketed in same manner as RSAs.  Demand deposits and passbook savings accounts warrant special mention. Generally considered rate-insensitive (act as core deposits), but there are arguments for their inclusion as rate-sensitive liabilities.

McGraw-Hill/Irwin 8-12 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. CGAP Ratio  May be useful to express CGAP in ratio form as, CGAP/Assets. Provides direction of exposure and Scale of the exposure.  Example: CGAP/A = $15 million / $270 million = 0.56, or 5.6 percent.

McGraw-Hill/Irwin 8-13 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Equal Rate Changes on RSAs, RSLs  Example: Suppose rates rise 2% for RSAs and RSLs. Expected annual change in NII,  NII = CGAP ×  R = $15 million ×.01 = $150,000  With positive CGAP, rates and NII move in the same direction.  Change proportional to CGAP

McGraw-Hill/Irwin 8-14 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Unequal Changes in Rates  If changes in rates on RSAs and RSLs are not equal, the spread changes. In this case,  NII = (RSA ×  R RSA ) - (RSL ×  R RSL )

McGraw-Hill/Irwin 8-15 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Unequal Rate Change Example  Spread effect example: RSA rate rises by 1.2% and RSL rate rises by 1.0%  NII =  interest revenue -  interest expense = ($155 million × 1.2%) - ($155 million × 1.0%) = $310,000

McGraw-Hill/Irwin 8-16 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Restructuring Assets & Liabilities  The FI can restructure its assets and liabilities, on or off the balance sheet, to benefit from projected interest rate changes. Positive gap: increase in rates increases NII Negative gap: decrease in rates increases NII Example: State Street Boston  Good luck?  Or Good Management?

McGraw-Hill/Irwin 8-17 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Weaknesses of Repricing Model  Weaknesses: Ignores market value effects and off-balance sheet (OBS) cash flows Overaggregative  Distribution of assets & liabilities within individual buckets is not considered. Mismatches within buckets can be substantial. Ignores effects of runoffs  Bank continuously originates and retires consumer and mortgage loans. Runoffs may be rate-sensitive.

McGraw-Hill/Irwin 8-18 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. The Maturity Model  Explicitly incorporates market value effects.  For fixed-income assets and liabilities: Rise (fall) in interest rates leads to fall (rise) in market price. The longer the maturity, the greater the effect of interest rate changes on market price. Fall in value of longer-term securities increases at diminishing rate for given increase in interest rates.

McGraw-Hill/Irwin 8-19 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Maturity of Portfolio  Maturity of portfolio of assets (liabilities) equals weighted average of maturities of individual components of the portfolio.  Principles stated on previous slide apply to portfolio as well as to individual assets or liabilities.  Typically, maturity gap, M A - M L > 0 for most banks and thrifts.

McGraw-Hill/Irwin 8-20 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Effects of Interest Rate Changes  Size of the gap determines the size of interest rate change that would drive net worth to zero.  Immunization and effect of setting M A - M L = 0.

McGraw-Hill/Irwin 8-21 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Maturities and Interest Rate Exposure  If M A - M L = 0, is the FI immunized? Extreme example: Suppose liabilities consist of 1-year zero coupon bond with face value $100. Assets consist of 1-year loan, which pays back $99.99 shortly after origination, and 1¢ at the end of the year. Both have maturities of 1 year. Not immunized, although maturity gap equals zero. Reason: Differences in duration* *(See Chapter 9)

McGraw-Hill/Irwin 8-22 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Maturity Model  Leverage also affects ability to eliminate interest rate risk using maturity model Example: Assets: $100 million in one-year 10-percent bonds, funded with $90 million in one-year 10- percent deposits (and equity) Maturity gap is zero but exposure to interest rate risk is not zero.

McGraw-Hill/Irwin 8-23 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration  The average life of an asset or liability  The weighted-average time to maturity using present value of the cash flows, relative to the total present value of the asset or liability as weights.

McGraw-Hill/Irwin 8-24 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. *Term Structure of Interest Rates YTM Time to Maturity YTM

McGraw-Hill/Irwin 8-25 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. *Unbiased Expectations Theory  Yield curve reflects market’s expectations of future short-term rates.  Long-term rates are geometric average of current and expected short-term rates. _ _ ~ ~ R N = [(1+R 1 )(1+E(r 2 ))…(1+E(r N ))] 1/N - 1

McGraw-Hill/Irwin 8-26 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. *Liquidity Premium Theory  Allows for future uncertainty.  Premium required to hold long-term.

McGraw-Hill/Irwin 8-27 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. *Market Segmentation Theory  Investors have specific needs in terms of maturity.  Yield curve reflects intersection of demand and supply of individual maturities.

McGraw-Hill/Irwin 8-28 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Pertinent Websites  For information related to central bank policy, visit: Bank for International Settlements: Federal Reserve Bank: